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<b>let </b><font color="Maroon" title="c4">P</font>, <font color="Maroon" title="c5">Q</font> be   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:64_1_2"/><i><font color="Green" title="E33">A3</font></i>: 
for <font color="Olive" title="b1">uu</font>, <font color="Olive" title="b2">vv</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">uu</font>,<font color="Olive" title="b2">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> iff  ex <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">uu</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">vv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font>,<font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 <b>and </b><br/><a NAME="E2:64_1_2"/><i><font color="Green" title="E34">A4</font></i>: 
for <font color="Olive" title="b1">uu</font>, <font color="Olive" title="b2">vv</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">uu</font>,<font color="Olive" title="b2">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Q</font> iff  ex <font color="Olive" title="b3">u1</font>, <font color="Olive" title="b4">u2</font>, <font color="Olive" title="b5">v1</font>, <font color="Olive" title="b6">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Olive" title="b1">uu</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">vv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">u1</font>,<font color="Olive" title="b4">u2</font>,<font color="Olive" title="b5">v1</font>,<font color="Olive" title="b6">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 ;<br/>

<a NAME="E3:64_1_2"/>
for <font color="Olive" title="b1">uu</font>, <font color="Olive" title="b2">vv</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">uu</font>,<font color="Olive" title="b2">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">uu</font>,<font color="Olive" title="b2">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Q</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">uu</font>, <font color="Maroon" title="c7">vv</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<a NAME="E1:64_1_2_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">uu</font>,<font color="Maroon" title="c7">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> iff  ex <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">u2</font>, <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> st <br/>( <font color="Maroon" title="c6">uu</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c7">vv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">u2</font>,<font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> ) )
 
<b>by </b><i><a class="txt" href="analort.html#E1:64_1_2"><i><font color="Green" title="E33">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:64_1_2_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">uu</font>,<font color="Maroon" title="c7">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">uu</font>,<font color="Maroon" title="c7">vv</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Q</font> )
 <b>by </b><i><a class="txt" href="analort.html#E2:64_1_2"><i><font color="Green" title="E34">A4</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:64_1_2"/>
<font color="Maroon" title="c4">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</a></i>;<br/>


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